Let G be a finite group. The prime degree graph of G, denoted by D (G), is an undirected graph whose vertex set is r (G) and there is an edge between two distinct primes p and q if and only if pq divides some irreducible character degree of G. In general, it seems that the prime graphs contain many edges and thus they should have many triangles, so one of the cases that would be interesting is to consider those finite groups whose prime degree graphs have a small number of triangles. In this paper we consider the case where for a nonsolvable group G, D (G) is a connected graph which has only one triangle and four vertices.

The structure and style of the Arabic ode was first standardized around traditional patterns. Through the ages, however, some of its features were challenged and then shifted. Due to the emergence of other types of poetic frameworks based on folkloric patterns which were quite diverse, harmoniously charming, and had. the wonderful capacity to express passionately lovelorn emotions and to describe natural beauties, the ancient ode style was severely challenged. During the contemporary period, however, the third side of this triangle of shift is being completed. . It is a shift that tries to make the internal and external characteristics of the oldest and greatest pattern of Arabic verse different and innovative

We establish the existence of two rigid triples of conjugacy classes in the algebraic group G2 in characteristic 5, complementing results of the second author with Liebeck and Marion. As a corollary, the finite groups G2(5n) are not (2; 4; 5)-generated, conrming a conjecture of Marion in this case.

Given a set $P$ of $n$ points in the plane, the maximum triangle problem asks for finding a triangle with three vertices in $P$ that encloses the maximum number of points from $P$. While the problem is easily solvable in $O(n^3)$ time, it has been open whether a subcubic solution is possible. In this paper, we show that the problem can be solved in $o(n^3)$ time, using a reduction to min-plus matrix multiplication. We also provide some improved approximation algorithms for the problem, including a 4-approximation algorithm running in $O(n \log n \log h)$ time, and a 3-approximation algorithm with $O(nh \log n + nh^2)$ runtime, where $h$ is the size of the convex hull of $P$.

Given a set $P$ of $n$ points in the plane, the maximum triangle problem asks for finding a triangle with three vertices in $P$ that encloses the maximum number of points from $P$. While the problem is easily solvable in $O(n^3)$ time, it has been open whether a subcubic solution is possible. In this paper, we show that the problem can be solved in $o(n^3)$ time, using a reduction to min-plus matrix multiplication. We also provide some improved approximation algorithms for the problem, including a 4-approximation algorithm running in $O(n \log n \log h)$ time, and a 3-approximation algorithm with $O(nh \log n + nh^2)$ runtime, where $h$ is the size of the convex hull of $P$.

A non-contradictible axiomatic theory is constructed under the local reversibility of the metric trian-gle inequality. The obtained notion includes the metric spaces as particular cases and the generated metric topology is T1-separated and generally, non-Hausdor .

Studying the Impact of Changes in triangle Confirmation of Financial Statements (Chief Financial Officer, Managing Director and Auditor) on Trial Members' Survival Rates Given the economic aspects of information, financial reporting and the accounting system play a vital role in the capital market. triangle is the confirmation of financial statements on the survival rate of triangle members. The purpose of this study is applied and methodological is causal research. The statistical population of the study is listed companies in Tehran Stock Exchange and using systematic sampling method, 166 companies are selected as the sample of the research and its period is between 2014 to 2019. In this study, panel data model was used. The results showed that the change in each of the triangle members had a significant effect on the survival rate of the other triangle members. By replacing the CEO, the financial survival of the company will be reduced, and vice versa. And replacing the auditor will reduce the CEO's survival rate, but replacing the CEO will increase the auditor's survival rate. The replacement of the auditor also reduced the financial manager's survival rate, but changes in the auditor's survival rate were not significant if the financial manager was replaced.